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Although gears can be manufactured using a wide variety of profiles, the involute curve is the most commonly used. Here are some of the basics.
What is so unique about gear manufacturing and inspection? Machining is mostly associated with making either flat or cylindrical shapes. These shapes can be created by a machine's simple linear or circular movements, but an involute curve is neither a straight line nor a circle. In fact, each point of the involute curve has a different radius and center of curvature. Is it necessary to go beyond simple circular and linear machine movements in order to create an involute curve? One of the unique features of the involute is the fact that it can be generated by linking circular and linear movements. This uniqueness has become fertile soil for many inventions that have simplified gear manufacturing and inspection. As is the case with gear generating machines, the traditional involute inspection machines take advantage of some of the involute properties. Even today, when computers can synchronize axes for creating any curve, taking advantage of involute properties can be very helpful. I t can simplify synchronization of machine movements and reduce the number of variables to monitor.
In designing involute gear teeth, it is essential that the fundamental properties of the involute curve be clearly understood. A review of "the Fundamental Laws of the Involute Curve" found in last issue will help in this respect. It has previously been shown that the involute curve has its origin at the base circle. Its length, however, may be anything from zero at the origin or starting point on to infinity. The problem, therefore, in designing gear teeth, is to select that portion of the involute, which will best meet all requirements.
Involute Curve Fundamentals. Over the years many different curves have been considered for the profile of a gear tooth. Today nearly every gear tooth uses as involute profile. The involute curve may be described as the curve generated by the end of a string that is unwrapped from a cylinder. (See Fig. 1) The circumference of the cylinder is called the base circle.
Can a gear profile generated by the hobbing method be an ideal involute? In strictly theoretical terms - no, but in practicality - yes. A gear profile generated by the hobbing method is an approximation of the involute curve. Let's review a classic example of an approximation.
Combining involute curves and body curves, merging factory and fashion, Winzeler Gear has transformed one of its products into gear haute couture. Winzeler Gear has created a plastic gear dress.
In the last section, we discussed gear inspection; the types of errors found by single and double flank composite and analytical tests; involute geometry; the involute cam and the causes and symptoms of profile errors. In this section, we go into tooth alignment and line of contact issues including lead, helix angles, pitch, pitchline runout, testing and errors in pitch and alignment.
It is very common for those working in the gear manufacturing industry to have only a limited understanding of the fundamental principals of involute helicoid gear metrology, the tendency being to leave the topic to specialists in the gear lab. It is well known that quiet, reliable gears can only be made using the information gleaned from proper gear metrology.
The American Society of Mechanical Engineers (ASME) announced at Gear Expo '95 that a national service for the calibration of involute artifacts is now available at the Department of Energy's Y-12 Plant in Oak Ridge, TN.
Early in the practice of involute gearing, virtually all gears were made with the teeth in a standard relationship to the reference pitch circle. This has the advantages that any two gears of the same pitch, helix angle and pressure angle can operate together, and that geometry calculations are relatively simple. It was soon realized, though, that there are greater advantages to be gained by modifying the relationship of the teeth to the reference pitch circle. The modifications are called profile shift.
Flute Index Flute index or spacing is defined as the variation from the desired angle between adjacent or nonadjacent tooth faces measured in a plane of rotation. AGMA defines and provides tolerance for adjacent and nonadjacent flute spacing errors. In addition, DIN and ISO standards provide tolerances for individual flute variation (Fig. 1).
Measurement institutions of seven different countries — China, Germany, Japan, Thailand, Ukraine, United Kingdom and the U.S. — participated in the implementation of the first international comparison of involute gear measurement standards. The German metrology institute Physikalisch-Technische Bundesanstalt (PTB) was chosen as the pilot laboratory as well as the organizer. Three typical involute gear measurement standards provided by the PTB were deployed for this comparison: a profile, a helix and a pitch measurement standard. In the final analysis, of the results obtained from all participants, the weighted mean was evaluated as reference value for all 28 measured parameters. However, besides the measurement standards, the measured parameters, and, most importantly, some of the comparison results from all participants are anonymously presented. Furthermore, mishandling of the measurement standards as occurred during the comparison will be illustrated.
The curved tooth cylindrical gear is one of ancient design. Samples which date from the period of the Warring State (475-221 BC) have been excavated from archeological sites in China. One such sample is now on display in the Xi'an Clay figures of Warriors and Horses Exhibition Hall. This example is about 3/4" in diameter and made of bronze. It was used in the famous model, "Ancient Chinese Vehicle With a Wooden Figure Always Pointing to the South." Although this early gear is handmade and somewhat crude, it is a viable model.
Noncircular gearing is not new. There are well-documented articles covering standard and high order elliptical gears, sinusoidal gears, logarithmic spiral gears, and circular gears mounted eccentrically. What these designs have in common is a pitch curve defined by a mathematical function. This article will cover noncircular gearing with free-form pitch curves, which, of course, includes all the aforementioned functions. This article also goes into the generation of teeth on the pitch curve, which is not usually covered in the technical literature. Needless to say, all this is possible only with the help of a computer.
Curved face width (CFW) spur gears are not popular in the gear industry. But these non-metallic gears have advantages over standard spur gears: higher contact ratio, higher tooth stiffness, and lower contact and bending stresses.
Beginning with our June Issue, Gear Technology is pleased to present a series of full-length chapters excerpted from Dr. Hermann J. Stadtfeld’s latest scholarly — yet practical — contribution to the gear industry — Gleason Bevel Gear Technology. Released in March, 2014 the book boasts 365 figures intended to add graphic support of a better understanding and easier recollection of the covered material.
Our experts tackle the topic of measuring involute masters, including both master gears and gear inspection artifacts.
Introduction The standard profile form in cylindrical gears is an involute. Involutes are generated with a trapezoidal rack — the basis for easy and production-stable manufacturing (Fig. 1).
This paper presents approximate and accurate methods to generate solid models of involute cylindrical gears using Autodesk Inventor 3-D CAD software.
The finished gear engineer, the man who is prepared for all emergencies, must first of all know the basic design principles. Next he must be well versed in all sorts of calculations which come under the heading of "involute trigonometry."
Involute spline couplings are used to transmit torque from a shaft to a gear hub or other rotating component. External gear teeth on the shaft engage an equal number of internal teeth in the hub. Because multiple teeth engage simultaneously, they can transmit much larger torques than a simple key and keyway assembly. However, manufacturing variations affect the clearance between each pair of mating teeth, resulting in only partial engagement.
Experience has proven that the involute provides the most satisfactory profile for spur and helical gear teeth, and fulfills the requirements for transmitting smooth, uniform angular motion.
This paper presents a unique approach and methodology to define the limits of selection for gear parameters. The area within those limits is called the “area of existence of involute gears” (Ref. 1). This paper presents the definition and construction of areas of existence of both external and internal gears. The isograms of the constant operating pressure angles, contact ratios and the maximum mesh efficiency (minimum sliding) isograms, as well as the interference isograms and other parameters are defined. An area of existence allows the location of gear pairs with certain characteristics. Its practical purpose is to define the gear pair parameters that satisfy specific performance requirements before detailed design and calculations. An area of existence of gears with asymmetric teeth is also considered.
Conical involute gears, also known as beveloid gears, are generalized involute gears that have the two flanks of the same tooth characterized by different base cylinder radii and different base helix angles.
It may not be widely recognized that most of the inspection data supplied by inspection equipment, following the practices of AGMA Standard 2015 and similar standards, are not of elemental accuracy deviations but of some form of composite deviations. This paper demonstrates the validity of this “composite” label by first defining the nature of a true elemental deviation and then, by referring to earlier literature, demonstrating how the common inspection practices for involute, lead (on helical gears), pitch, and, in some cases, total accumulated pitch, constitute composite measurements.
Conical involute gears (beveloids) are used in transmissions with intersecting or skewed axes and for backlash-free transmissions with parallel axes.
In our last issue, the labels on the drawings illustrating "Involutometry" by Harlan Van Gerpan and C. Kent Reece were inadvertently omitted. For your convenience we have reproduced the corrected illustrations here. We regret any inconvenience this may have caused our readers.
Gears are toothed wheels used primarily to transmit motion and power between rotating shafts. Gearing is an assembly of two or more gears. The most durable of all mechanical drives, gearing can transmit high power at efficiencies approaching 0.99 and with long service life. As precision machine elements gears must be designed.
Question: I have just become involved with the inspection of gears in a production operation and wonder why the procedure specifies that four involute checks must be made on each side of the tooth of the gear being produced, where one tooth is checked and charted in each quadrant of the gear. Why is this done? These particular gears are checked in the pre-shaved, finish-shaved, and the after-heat-treat condition, so a lot of profile checking must be done.
Spur gear endurance tests were conducted to investigate the surface pitting fatigue life of noninvolute gears with low numbers of teeth and low contact ratios for the use in advanced application. The results were compared with those for a standard involute design with a low number of teeth. The gear pitch diameter was 8.89 cm (3.50 in.) with 12 teeth on both gear designs. Test conditions were an oil inlet temperature of 320 K (116 degrees F), a maximum Hertz stress of 1.49 GPa (216 ksi), and a speed of 10,000 rpm. The following results were obtained: The noninvolute gear had a surface pitting fatigue life approximately 1.6 times that of the standard involute gear of a similar design. The surface pitting fatigue life of the 3.43-pitch AISI 8620 noninvolute gear was approximately equal to the surface pitting fatigue life of an 8-pitch, 28-tooth AISI 9310 gear at the same load, but at a considerably higher maximum Hertz stress.
A universal gear is one generated by a common rack on a cylindrical, conical, or planar surface, and whose teeth can be oriented parallel or skewed, centered, or offset, with respect to its axes. Mating gear axes can be parallel or crossed, non-intersecting or intersecting, skewed or parallel, and can have any angular orientation (See Fig.1) The taper gear is a universal gear. It provides unique geometric properties and a range of applications unmatched by any other motion transmission element. (See Fig.2) The taper gear can be produced by any rack-type tool generator or hobbing machine which has a means of tilting the cutter or work axis and/or coordinating simultaneous traverse and infeed motions.
Engineering design requires many different types of gears and splines. Although these components are rather expensive, subject to direct wear, and difficult to replace, transmissions with gears and splines are required for two very simple reasons: 1) Motors have an unfavorable (disadvantageous) relation of torque to number of revolutions. 2)Power is usually required to be transmitted along a shaft.
In principal, the design of internal helical gear teeth is the same as that for external helical gears. Any of the basic rack forms used for external helical gears may be applied to internal helical gears. The internal gear drive, however, has several limitations; not only all those which apply to external gears, but also several others which are peculiar to internal gears. As with external gears, in order to secure effective tooth action, interferences must be avoided. The possible interferences on an internal gear drive are as follows: 1. Involute interference. To avoid this, all of the working profile of the internal tooth must be of involute form.
On many occasions a reasonably approximate, but not exact, representation of an involute tooth profile is required. Applications include making drawings, especially at enlarged scale, and laser or EDM cutting of gears, molds, and dies used to produce gears. When numerical control (NC) techniques are to be used, a simple way to model an involute can make the NC programming task much easier.
Question: Do machines exist that are capable of cutting bevel gear teeth on a gear of the following specifications: 14 teeth, 1" circular pitch, 14.5 degrees pressure angle, 4 degrees pitch cone angle, 27.5" cone distance, and an 2.5" face width?